Analysis of BiPOCD data
Sebastian Sauer
4 Juli 2016
- 1 First glimpse
- 2 Overviews
- 3 Bivariate assocations
- 4 Most important variables (narrow data set)
- 5 Interocular Trauma Test
1 First glimpse
2 Overviews
2.1 Summaries of quantitative variables
2.2 Histograms of quantitative variables
2.3 Histogram of non-numeric variables
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2.4 Check for (near) zero variance (nz/nzv) variables
Predictors without (much) variance do not add to the model. Better exclude them, at least know them.
2.6 Missing values
2.7 Checking Scale quality
Scale quality involves aspects as intercorrelation of items of a scale, internal consisteny, score distribution, and the like. Let’s see.
2.7.1 Univariate distributions of sum scores
Let’s check the distribution for the sum scores variables (which are: CYBOCS_pre_sum, ChOCI_R_C_sumsym_PRE, ChOCI_R_C_sumimp_PRE, EWSASC_sum_PRE, SCAS_S_C_sum_PRE, CDI_S_sum_PRE, ChOCI_R_P_sumsym_PRE, ChOCI_R_P_sumimp_PRE, FAS_PR_sum_PRE, EWSASP_sum_PRE, SCAS_S_P_sum_PRE.
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2.7.2 Correlation of comorbidity
If one suffers from one comorbidity, does he/she suffer (in general) from other comorbidities too? NZV variables are excluded.
We should do this more stringently, but let’s start with a brief look to the items of ChOCI, to see whether they are correlated (as they should be, at least for common subscale-items). Those are quite a few.
2.7.3 ChOCI
##
## Reliability analysis
## Call: psych::alpha(x = ChOCI_items, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N
## 0.86 0.91 1 0.14 11
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N
## ChOCI_R_C_1_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_2_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_3_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_4_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_5_PRE 0.86 0.92 1 0.14 11
## ChOCI_R_C_6_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_7_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_C_8_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_9_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_10_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_C_12_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_C_13_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_C_14_PRE 0.86 0.91 1 0.14 10
## ChOCI_R_C_15_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_16_PRE 0.86 0.91 1 0.14 10
## ChOCI_R_C_17_PRE 0.86 0.91 1 0.14 10
## ChOCI_R_C_18_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_19_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_20_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_C_21_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_22_PRE 0.86 0.91 1 0.14 10
## ChOCI_R_C_23_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_24_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_25_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_26_PRE- 0.86 0.92 1 0.14 11
## ChOCI_R_C_27_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_29_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_30_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_31_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_32_PRE 0.86 0.92 1 0.14 11
## ChOCI_R_C_33_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_34_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_C_sumsym_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_C_sumimp_PRE 0.85 0.91 1 0.13 10
## ChOCI_R_P_1_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_2_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_3_PRE 0.86 0.92 1 0.14 11
## ChOCI_R_P_4_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_5_PRE 0.86 0.92 1 0.14 11
## ChOCI_R_P_6_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_7_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_8_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_9_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_10_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_12_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_P_13_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_P_14_PRE 0.86 0.91 1 0.14 10
## ChOCI_R_P_15_PRE 0.86 0.92 1 0.14 11
## ChOCI_R_P_16_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_17_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_P_18_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_19_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_20_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_21_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_22_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_23_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_24_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_25_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_26_PRE 0.86 0.92 1 0.14 11
## ChOCI_R_P_27_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_29_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_30_PRE 0.86 0.91 1 0.14 10
## ChOCI_R_P_31_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_32_PRE 0.86 0.92 1 0.14 11
## ChOCI_R_P_33_PRE 0.86 0.91 1 0.14 11
## ChOCI_R_P_34_PRE 0.86 0.91 1 0.13 10
## ChOCI_R_P_sumsym_PRE 0.85 0.91 1 0.13 10
## ChOCI_R_P_sumimp_PRE 0.87 0.91 1 0.13 10
##
## Item statistics
## r r.cor r.drop
## ChOCI_R_C_1_PRE 0.410 0.410 0.405
## ChOCI_R_C_2_PRE 0.278 0.278 0.240
## ChOCI_R_C_3_PRE 0.383 0.383 0.353
## ChOCI_R_C_4_PRE 0.385 0.385 0.354
## ChOCI_R_C_5_PRE 0.098 0.098 0.066
## ChOCI_R_C_6_PRE 0.322 0.322 0.296
## ChOCI_R_C_7_PRE 0.521 0.521 0.450
## ChOCI_R_C_8_PRE 0.246 0.246 0.188
## ChOCI_R_C_9_PRE 0.275 0.275 0.223
## ChOCI_R_C_10_PRE 0.612 0.612 0.602
## ChOCI_R_C_12_PRE 0.619 0.619 0.642
## ChOCI_R_C_13_PRE 0.659 0.659 0.667
## ChOCI_R_C_14_PRE 0.468 0.468 0.447
## ChOCI_R_C_15_PRE 0.317 0.317 0.296
## ChOCI_R_C_16_PRE 0.504 0.504 0.485
## ChOCI_R_C_17_PRE 0.477 0.477 0.493
## ChOCI_R_C_18_PRE 0.356 0.356 0.293
## ChOCI_R_C_19_PRE 0.351 0.351 0.293
## ChOCI_R_C_20_PRE 0.573 0.573 0.531
## ChOCI_R_C_21_PRE 0.369 0.369 0.357
## ChOCI_R_C_22_PRE 0.470 0.470 0.436
## ChOCI_R_C_23_PRE 0.279 0.279 0.241
## ChOCI_R_C_24_PRE 0.329 0.329 0.277
## ChOCI_R_C_25_PRE 0.361 0.361 0.302
## ChOCI_R_C_26_PRE- -0.019 -0.019 -0.012
## ChOCI_R_C_27_PRE 0.410 0.410 0.383
## ChOCI_R_C_29_PRE 0.345 0.345 0.344
## ChOCI_R_C_30_PRE 0.465 0.465 0.474
## ChOCI_R_C_31_PRE 0.354 0.354 0.336
## ChOCI_R_C_32_PRE 0.133 0.133 0.095
## ChOCI_R_C_33_PRE 0.444 0.444 0.461
## ChOCI_R_C_34_PRE 0.390 0.390 0.401
## ChOCI_R_C_sumsym_PRE 0.749 0.749 0.598
## ChOCI_R_C_sumimp_PRE 0.768 0.768 0.720
## ChOCI_R_P_1_PRE 0.366 0.366 0.366
## ChOCI_R_P_2_PRE 0.379 0.379 0.344
## ChOCI_R_P_3_PRE 0.154 0.154 0.117
## ChOCI_R_P_4_PRE 0.373 0.373 0.350
## ChOCI_R_P_5_PRE 0.215 0.215 0.191
## ChOCI_R_P_6_PRE 0.336 0.336 0.332
## ChOCI_R_P_7_PRE 0.261 0.261 0.201
## ChOCI_R_P_8_PRE 0.245 0.245 0.216
## ChOCI_R_P_9_PRE 0.224 0.224 0.170
## ChOCI_R_P_10_PRE 0.452 0.452 0.432
## ChOCI_R_P_12_PRE 0.521 0.521 0.539
## ChOCI_R_P_13_PRE 0.525 0.525 0.557
## ChOCI_R_P_14_PRE 0.480 0.480 0.499
## ChOCI_R_P_15_PRE 0.199 0.199 0.183
## ChOCI_R_P_16_PRE 0.449 0.449 0.463
## ChOCI_R_P_17_PRE 0.552 0.552 0.577
## ChOCI_R_P_18_PRE 0.363 0.363 0.294
## ChOCI_R_P_19_PRE 0.391 0.391 0.364
## ChOCI_R_P_20_PRE 0.377 0.377 0.316
## ChOCI_R_P_21_PRE 0.264 0.264 0.253
## ChOCI_R_P_22_PRE 0.289 0.289 0.228
## ChOCI_R_P_23_PRE 0.389 0.389 0.357
## ChOCI_R_P_24_PRE 0.381 0.381 0.321
## ChOCI_R_P_25_PRE 0.308 0.308 0.243
## ChOCI_R_P_26_PRE 0.162 0.162 0.106
## ChOCI_R_P_27_PRE 0.289 0.289 0.237
## ChOCI_R_P_29_PRE 0.396 0.396 0.414
## ChOCI_R_P_30_PRE 0.471 0.471 0.508
## ChOCI_R_P_31_PRE 0.421 0.421 0.446
## ChOCI_R_P_32_PRE 0.181 0.181 0.189
## ChOCI_R_P_33_PRE 0.232 0.232 0.250
## ChOCI_R_P_34_PRE 0.540 0.540 0.575
## ChOCI_R_P_sumsym_PRE 0.752 0.752 0.621
## ChOCI_R_P_sumimp_PRE 0.624 0.624 0.5542.7.4 CYBOCS
## # A tibble: 61 x 5
## CYBOCS_pre_OBS CYBOCS_pre_COMP CYBOCS_pre_insight CYBOCS_pre_avoid
## <int> <int> <int> <int>
## 1 10 12 2 1
## 2 12 15 1 1
## 3 12 13 1 1
## 4 12 12 1 2
## 5 13 13 3 3
## 6 11 10 2 2
## 7 11 11 2 1
## 8 9 9 2 1
## 9 8 8 0 0
## 10 15 14 2 2
## # ... with 51 more rows, and 1 more variables: CYBOCS_3m <int>2.7.5 EWSASC
##
## Reliability analysis
## Call: psych::alpha(x = data.frame(EWSASC_items))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.86 0.86 0.88 0.55 6.2 0.028 3 1.9
##
## lower alpha upper 95% confidence boundaries
## 0.81 0.86 0.92
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N
## EWSASC_schoolandwork_PRE 0.87 0.87 0.89 0.63 6.9
## EWSASC_everydaysituations_PRE 0.88 0.87 0.89 0.62 6.7
## EWSASC_social_PRE 0.78 0.78 0.76 0.47 3.6
## EWSASC_leisuretime_PRE 0.79 0.78 0.76 0.48 3.6
## EWSASC_family_PRE 0.83 0.83 0.85 0.55 4.9
## alpha se
## EWSASC_schoolandwork_PRE 0.028
## EWSASC_everydaysituations_PRE 0.026
## EWSASC_social_PRE 0.045
## EWSASC_leisuretime_PRE 0.045
## EWSASC_family_PRE 0.035
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## EWSASC_schoolandwork_PRE 61 0.67 0.68 0.54 0.51 3.4 2.1
## EWSASC_everydaysituations_PRE 61 0.70 0.69 0.55 0.52 3.5 2.5
## EWSASC_social_PRE 61 0.92 0.92 0.97 0.87 2.6 2.5
## EWSASC_leisuretime_PRE 61 0.92 0.91 0.96 0.86 2.6 2.5
## EWSASC_family_PRE 61 0.80 0.80 0.73 0.68 2.7 2.2
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 6 7 8
## EWSASC_schoolandwork_PRE 0.05 0.10 0.26 0.20 0.13 0.07 0.07 0.10 0.03
## EWSASC_everydaysituations_PRE 0.16 0.08 0.18 0.05 0.15 0.05 0.23 0.07 0.03
## EWSASC_social_PRE 0.28 0.15 0.15 0.11 0.07 0.08 0.07 0.07 0.03
## EWSASC_leisuretime_PRE 0.28 0.16 0.13 0.11 0.07 0.07 0.07 0.08 0.03
## EWSASC_family_PRE 0.20 0.16 0.16 0.15 0.13 0.07 0.07 0.05 0.02
## miss
## EWSASC_schoolandwork_PRE 0
## EWSASC_everydaysituations_PRE 0
## EWSASC_social_PRE 0
## EWSASC_leisuretime_PRE 0
## EWSASC_family_PRE 0Good.
2.7.6 SCAS
##
## Reliability analysis
## Call: psych::alpha(x = data.frame(SCAS_items))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.86 0.87 0.93 0.21 6.5 0.025 0.99 0.44
##
## lower alpha upper 95% confidence boundaries
## 0.81 0.86 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## SCAS_S_C_1_PRE 0.86 0.86 0.93 0.22 6.4 0.026
## SCAS_S_C_2_PRE 0.86 0.86 0.92 0.21 6.1 0.027
## SCAS_S_C_3_PRE 0.86 0.86 0.93 0.21 6.2 0.027
## SCAS_S_C_4_PRE 0.85 0.86 0.92 0.21 6.1 0.027
## SCAS_S_C_5_PRE 0.86 0.86 0.93 0.21 6.2 0.026
## SCAS_S_C_6_PRE 0.86 0.86 0.93 0.21 6.2 0.027
## SCAS_S_C_7_PRE 0.86 0.86 0.93 0.21 6.2 0.027
## SCAS_S_C_8_PRE 0.86 0.86 0.93 0.22 6.3 0.026
## SCAS_S_C_9_PRE 0.86 0.86 0.93 0.21 6.2 0.027
## SCAS_S_C_10_PRE 0.86 0.86 0.92 0.21 6.1 0.027
## SCAS_S_C_11_PRE 0.86 0.87 0.93 0.22 6.5 0.026
## SCAS_S_C_12_PRE 0.86 0.87 0.93 0.22 6.5 0.025
## SCAS_S_P_1_PRE 0.86 0.86 0.92 0.21 6.2 0.027
## SCAS_S_P_2_PRE 0.86 0.86 0.93 0.21 6.2 0.027
## SCAS_S_P_3_PRE 0.86 0.86 0.92 0.21 6.3 0.027
## SCAS_S_P_4_PRE 0.86 0.87 0.93 0.22 6.5 0.026
## SCAS_S_P_5_PRE 0.86 0.86 0.93 0.22 6.3 0.026
## SCAS_S_P_6_PRE 0.86 0.86 0.93 0.21 6.2 0.027
## SCAS_S_P_7_PRE 0.86 0.86 0.93 0.21 6.2 0.027
## SCAS_S_P_8_PRE 0.86 0.86 0.92 0.21 6.2 0.027
## SCAS_S_P_9_PRE 0.86 0.86 0.93 0.21 6.3 0.026
## SCAS_S_P_10_PRE 0.85 0.86 0.92 0.20 5.9 0.028
## SCAS_S_P_11_PRE 0.86 0.86 0.93 0.22 6.3 0.026
## SCAS_S_P_12_PRE 0.86 0.87 0.93 0.22 6.6 0.025
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## SCAS_S_C_1_PRE 61 0.43 0.42 0.41 0.36 1.03 0.91
## SCAS_S_C_2_PRE 61 0.57 0.58 0.57 0.51 0.85 0.83
## SCAS_S_C_3_PRE 61 0.56 0.55 0.54 0.50 1.57 0.96
## SCAS_S_C_4_PRE 61 0.58 0.59 0.57 0.53 0.54 0.79
## SCAS_S_C_5_PRE 61 0.50 0.51 0.49 0.43 1.02 0.94
## SCAS_S_C_6_PRE 61 0.51 0.51 0.49 0.45 1.59 0.88
## SCAS_S_C_7_PRE 61 0.52 0.52 0.50 0.46 0.79 0.90
## SCAS_S_C_8_PRE 61 0.48 0.47 0.45 0.40 1.56 1.01
## SCAS_S_C_9_PRE 61 0.53 0.54 0.53 0.47 0.56 0.87
## SCAS_S_C_10_PRE 61 0.57 0.57 0.57 0.50 0.64 0.91
## SCAS_S_C_11_PRE 61 0.39 0.38 0.33 0.31 1.16 0.97
## SCAS_S_C_12_PRE 61 0.38 0.37 0.34 0.29 1.26 1.06
## SCAS_S_P_1_PRE 61 0.51 0.51 0.50 0.44 0.87 0.94
## SCAS_S_P_2_PRE 61 0.52 0.52 0.51 0.46 0.82 0.85
## SCAS_S_P_3_PRE 61 0.51 0.50 0.50 0.44 1.52 0.98
## SCAS_S_P_4_PRE 61 0.37 0.37 0.35 0.29 0.56 0.94
## SCAS_S_P_5_PRE 61 0.47 0.48 0.44 0.40 0.93 0.85
## SCAS_S_P_6_PRE 61 0.55 0.55 0.54 0.49 1.54 0.91
## SCAS_S_P_7_PRE 61 0.53 0.54 0.52 0.46 0.61 0.90
## SCAS_S_P_8_PRE 61 0.52 0.51 0.51 0.45 1.26 1.03
## SCAS_S_P_9_PRE 61 0.46 0.48 0.46 0.41 0.34 0.57
## SCAS_S_P_10_PRE 61 0.68 0.70 0.69 0.64 0.44 0.74
## SCAS_S_P_11_PRE 61 0.45 0.46 0.43 0.38 0.89 0.91
## SCAS_S_P_12_PRE 61 0.29 0.29 0.25 0.21 1.30 0.90
##
## Non missing response frequency for each item
## 0 1 2 3 miss
## SCAS_S_C_1_PRE 0.28 0.52 0.08 0.11 0
## SCAS_S_C_2_PRE 0.39 0.39 0.18 0.03 0
## SCAS_S_C_3_PRE 0.15 0.31 0.36 0.18 0
## SCAS_S_C_4_PRE 0.61 0.28 0.08 0.03 0
## SCAS_S_C_5_PRE 0.34 0.38 0.20 0.08 0
## SCAS_S_C_6_PRE 0.10 0.38 0.36 0.16 0
## SCAS_S_C_7_PRE 0.48 0.31 0.16 0.05 0
## SCAS_S_C_8_PRE 0.15 0.38 0.25 0.23 0
## SCAS_S_C_9_PRE 0.66 0.16 0.15 0.03 0
## SCAS_S_C_10_PRE 0.61 0.20 0.15 0.05 0
## SCAS_S_C_11_PRE 0.30 0.34 0.26 0.10 0
## SCAS_S_C_12_PRE 0.30 0.31 0.23 0.16 0
## SCAS_S_P_1_PRE 0.41 0.41 0.08 0.10 0
## SCAS_S_P_2_PRE 0.39 0.46 0.08 0.07 0
## SCAS_S_P_3_PRE 0.15 0.38 0.28 0.20 0
## SCAS_S_P_4_PRE 0.67 0.18 0.07 0.08 0
## SCAS_S_P_5_PRE 0.34 0.43 0.18 0.05 0
## SCAS_S_P_6_PRE 0.11 0.39 0.33 0.16 0
## SCAS_S_P_7_PRE 0.62 0.20 0.13 0.05 0
## SCAS_S_P_8_PRE 0.28 0.33 0.25 0.15 0
## SCAS_S_P_9_PRE 0.70 0.25 0.05 0.00 0
## SCAS_S_P_10_PRE 0.69 0.20 0.10 0.02 0
## SCAS_S_P_11_PRE 0.44 0.26 0.26 0.03 0
## SCAS_S_P_12_PRE 0.23 0.31 0.39 0.07 02.7.7 CDI
##
## Reliability analysis
## Call: psych::alpha(x = data.frame(CDI_items))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.81 0.81 0.86 0.28 4.2 0.035 0.4 0.31
##
## lower alpha upper 95% confidence boundaries
## 0.74 0.81 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## PanicDisorder 0.82 0.82 0.85 0.32 4.7 0.035
## CDI_S_1_PRE 0.79 0.78 0.83 0.26 3.6 0.039
## CDI_S_2_PRE 0.78 0.78 0.83 0.27 3.6 0.040
## CDI_S_3_PRE 0.80 0.80 0.84 0.28 3.9 0.037
## CDI_S_4_PRE 0.77 0.77 0.81 0.25 3.3 0.041
## CDI_S_5_PRE 0.79 0.79 0.83 0.27 3.8 0.038
## CDI_S_6_PRE 0.80 0.79 0.84 0.28 3.8 0.037
## CDI_S_7_PRE 0.79 0.79 0.84 0.27 3.7 0.039
## CDI_S_8_PRE 0.78 0.79 0.83 0.27 3.7 0.039
## CDI_S_9_PRE 0.80 0.80 0.85 0.29 4.1 0.036
## CDI_S_10_PRE 0.79 0.79 0.84 0.27 3.8 0.038
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## PanicDisorder 61 0.21 0.29 0.20 0.13 0.082 0.28
## CDI_S_1_PRE 61 0.64 0.67 0.64 0.54 0.328 0.51
## CDI_S_2_PRE 61 0.67 0.65 0.61 0.55 0.492 0.62
## CDI_S_3_PRE 61 0.52 0.55 0.49 0.41 0.393 0.49
## CDI_S_4_PRE 61 0.75 0.76 0.77 0.69 0.262 0.44
## CDI_S_5_PRE 61 0.59 0.59 0.56 0.49 0.197 0.44
## CDI_S_6_PRE 61 0.62 0.59 0.53 0.47 0.885 0.71
## CDI_S_7_PRE 61 0.64 0.62 0.55 0.52 0.623 0.58
## CDI_S_8_PRE 61 0.66 0.64 0.62 0.54 0.492 0.62
## CDI_S_9_PRE 61 0.51 0.49 0.42 0.37 0.508 0.57
## CDI_S_10_PRE 61 0.57 0.60 0.56 0.48 0.164 0.42
##
## Non missing response frequency for each item
## 0 1 2 miss
## PanicDisorder 0.92 0.08 0.00 0
## CDI_S_1_PRE 0.69 0.30 0.02 0
## CDI_S_2_PRE 0.57 0.36 0.07 0
## CDI_S_3_PRE 0.61 0.39 0.00 0
## CDI_S_4_PRE 0.74 0.26 0.00 0
## CDI_S_5_PRE 0.82 0.16 0.02 0
## CDI_S_6_PRE 0.31 0.49 0.20 0
## CDI_S_7_PRE 0.43 0.52 0.05 0
## CDI_S_8_PRE 0.57 0.36 0.07 0
## CDI_S_9_PRE 0.52 0.44 0.03 0
## CDI_S_10_PRE 0.85 0.13 0.02 0##
## Reliability analysis
## Call: psych::alpha(x = data.frame(FAS_items))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.91 0.92 0.94 0.48 11 0.016 1.4 0.95
##
## lower alpha upper 95% confidence boundaries
## 0.88 0.91 0.95
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## FAS_PR_1_PRE 0.91 0.92 0.94 0.50 11.0 0.017
## FAS_PR_2_PRE 0.90 0.91 0.93 0.47 9.6 0.019
## FAS_PR_3_PRE 0.91 0.91 0.94 0.49 10.5 0.017
## FAS_PR_4_PRE 0.91 0.91 0.94 0.49 10.7 0.017
## FAS_PR_5_PRE 0.91 0.91 0.93 0.48 10.1 0.017
## FAS_PR_6_PRE 0.91 0.91 0.93 0.47 9.8 0.018
## FAS_PR_7_PRE 0.91 0.91 0.93 0.47 9.9 0.018
## FAS_PR_8_PRE 0.91 0.91 0.93 0.48 10.1 0.017
## FAS_PR_9_PRE 0.90 0.91 0.93 0.47 9.8 0.018
## FAS_PR_10_PRE 0.91 0.91 0.93 0.48 10.1 0.018
## FAS_PR_11_PRE 0.91 0.91 0.93 0.48 10.1 0.017
## FAS_PR_12_PRE 0.91 0.91 0.94 0.48 10.0 0.018
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## FAS_PR_1_PRE 61 0.59 0.60 0.54 0.52 2.89 1.1
## FAS_PR_2_PRE 61 0.82 0.81 0.79 0.77 1.30 1.6
## FAS_PR_3_PRE 61 0.69 0.67 0.63 0.60 1.93 1.7
## FAS_PR_4_PRE 61 0.64 0.63 0.59 0.56 1.77 1.4
## FAS_PR_5_PRE 61 0.71 0.73 0.70 0.66 0.64 1.0
## FAS_PR_6_PRE 61 0.76 0.77 0.76 0.71 1.28 1.3
## FAS_PR_7_PRE 61 0.76 0.76 0.74 0.70 1.28 1.3
## FAS_PR_8_PRE 61 0.72 0.73 0.73 0.66 0.87 1.3
## FAS_PR_9_PRE 61 0.77 0.78 0.78 0.72 0.79 1.3
## FAS_PR_10_PRE 61 0.73 0.73 0.72 0.67 1.28 1.2
## FAS_PR_11_PRE 61 0.73 0.73 0.72 0.67 1.25 1.3
## FAS_PR_12_PRE 61 0.74 0.75 0.71 0.68 1.25 1.3
##
## Non missing response frequency for each item
## 0 1 2 3 4 miss
## FAS_PR_1_PRE 0.03 0.08 0.26 0.21 0.41 0
## FAS_PR_2_PRE 0.51 0.13 0.08 0.11 0.16 0
## FAS_PR_3_PRE 0.28 0.21 0.13 0.05 0.33 0
## FAS_PR_4_PRE 0.23 0.30 0.13 0.16 0.18 0
## FAS_PR_5_PRE 0.61 0.28 0.02 0.07 0.03 0
## FAS_PR_6_PRE 0.38 0.23 0.20 0.13 0.07 0
## FAS_PR_7_PRE 0.43 0.10 0.26 0.20 0.02 0
## FAS_PR_8_PRE 0.61 0.11 0.13 0.10 0.05 0
## FAS_PR_9_PRE 0.67 0.08 0.08 0.11 0.05 0
## FAS_PR_10_PRE 0.34 0.28 0.18 0.15 0.05 0
## FAS_PR_11_PRE 0.43 0.18 0.16 0.18 0.05 0
## FAS_PR_12_PRE 0.43 0.13 0.26 0.13 0.05 0##
## Reliability analysis
## Call: psych::alpha(x = data.frame(EWSASP_items))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.8 0.8 0.8 0.45 4 0.041 3.1 1.8
##
## lower alpha upper 95% confidence boundaries
## 0.72 0.8 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N
## EWSASP_schoolandwork_PRE 0.78 0.78 0.74 0.46 3.4
## EWSASP_everydaysituations_PRE 0.75 0.75 0.72 0.43 3.0
## EWSASP_social_PRE 0.75 0.75 0.72 0.42 2.9
## EWSASP_leisuretime_PRE 0.77 0.77 0.76 0.46 3.4
## EWSASP_family_PRE 0.77 0.77 0.72 0.46 3.4
## alpha se
## EWSASP_schoolandwork_PRE 0.047
## EWSASP_everydaysituations_PRE 0.053
## EWSASP_social_PRE 0.053
## EWSASP_leisuretime_PRE 0.048
## EWSASP_family_PRE 0.048
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## EWSASP_schoolandwork_PRE 61 0.72 0.72 0.63 0.54 4.0 2.5
## EWSASP_everydaysituations_PRE 61 0.79 0.78 0.71 0.63 3.5 2.6
## EWSASP_social_PRE 61 0.78 0.78 0.72 0.64 2.8 2.4
## EWSASP_leisuretime_PRE 61 0.71 0.73 0.62 0.56 1.8 2.2
## EWSASP_family_PRE 61 0.72 0.72 0.66 0.55 3.4 2.4
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 6 7 8
## EWSASP_schoolandwork_PRE 0.08 0.05 0.26 0.07 0.13 0.10 0.11 0.07 0.13
## EWSASP_everydaysituations_PRE 0.16 0.13 0.08 0.08 0.21 0.05 0.13 0.07 0.08
## EWSASP_social_PRE 0.23 0.13 0.21 0.10 0.07 0.05 0.15 0.02 0.05
## EWSASP_leisuretime_PRE 0.41 0.15 0.15 0.07 0.10 0.03 0.07 0.02 0.02
## EWSASP_family_PRE 0.18 0.08 0.10 0.16 0.15 0.08 0.16 0.05 0.03
## miss
## EWSASP_schoolandwork_PRE 0
## EWSASP_everydaysituations_PRE 0
## EWSASP_social_PRE 0
## EWSASP_leisuretime_PRE 0
## EWSASP_family_PRE 0##
## Reliability analysis
## Call: psych::alpha(x = data.frame(EWSASP_items))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.8 0.8 0.8 0.45 4 0.041 3.1 1.8
##
## lower alpha upper 95% confidence boundaries
## 0.72 0.8 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N
## EWSASP_schoolandwork_PRE 0.78 0.78 0.74 0.46 3.4
## EWSASP_everydaysituations_PRE 0.75 0.75 0.72 0.43 3.0
## EWSASP_social_PRE 0.75 0.75 0.72 0.42 2.9
## EWSASP_leisuretime_PRE 0.77 0.77 0.76 0.46 3.4
## EWSASP_family_PRE 0.77 0.77 0.72 0.46 3.4
## alpha se
## EWSASP_schoolandwork_PRE 0.047
## EWSASP_everydaysituations_PRE 0.053
## EWSASP_social_PRE 0.053
## EWSASP_leisuretime_PRE 0.048
## EWSASP_family_PRE 0.048
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## EWSASP_schoolandwork_PRE 61 0.72 0.72 0.63 0.54 4.0 2.5
## EWSASP_everydaysituations_PRE 61 0.79 0.78 0.71 0.63 3.5 2.6
## EWSASP_social_PRE 61 0.78 0.78 0.72 0.64 2.8 2.4
## EWSASP_leisuretime_PRE 61 0.71 0.73 0.62 0.56 1.8 2.2
## EWSASP_family_PRE 61 0.72 0.72 0.66 0.55 3.4 2.4
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 6 7 8
## EWSASP_schoolandwork_PRE 0.08 0.05 0.26 0.07 0.13 0.10 0.11 0.07 0.13
## EWSASP_everydaysituations_PRE 0.16 0.13 0.08 0.08 0.21 0.05 0.13 0.07 0.08
## EWSASP_social_PRE 0.23 0.13 0.21 0.10 0.07 0.05 0.15 0.02 0.05
## EWSASP_leisuretime_PRE 0.41 0.15 0.15 0.07 0.10 0.03 0.07 0.02 0.02
## EWSASP_family_PRE 0.18 0.08 0.10 0.16 0.15 0.08 0.16 0.05 0.03
## miss
## EWSASP_schoolandwork_PRE 0
## EWSASP_everydaysituations_PRE 0
## EWSASP_social_PRE 0
## EWSASP_leisuretime_PRE 0
## EWSASP_family_PRE 03 Bivariate assocations
3.1 Assocations of ChOCI sum scores and treatment response
3.2 Associations with treatment response
3.2.1 Comorbidity as predictors
The (non-nzv) comorbities are: Depression, PanicDisorder, SocialPhob, SpecificPhob, TourettesTics, ADHD, GAD, responder_3m_f. The Odds ratios of the comorbities with the outcome variable are: 1.48, 2.33, 0.95, 4.31, 0.45, 0.25, 1.5, 0. The odds are computed in favor of treatment success.
| ID | names_comorb | OR_comorb |
|---|---|---|
| 1 | Depression | 1.48 |
| 2 | PanicDisorder | 2.33 |
| 3 | SocialPhob | 0.95 |
| 4 | SpecificPhob | 4.31 |
| 5 | TourettesTics | 0.45 |
| 6 | ADHD | 0.25 |
| 7 | GAD | 1.50 |
| 8 | responder_3m_f | 0.00 |
The relative risks of the comorbities with the outcome variable are: 0, 0.38, 0.59, 0.97, 1.24, 1.25, 1.53, 1.94. Relativs Risks are also computed in favor of success (so, they depict rather relative protectino probabilities).
| ID | names_comorb | RR_comorb |
|---|---|---|
| 1 | Depression | 1.24 |
| 2 | PanicDisorder | 1.53 |
| 3 | SocialPhob | 0.97 |
| 4 | SpecificPhob | 1.94 |
| 5 | TourettesTics | 0.59 |
| 6 | ADHD | 0.38 |
| 7 | GAD | 1.25 |
| 8 | responder_3m_f | 0.00 |
Let’s plot the assocation of the comorbitity with the outcome var responder_3m. To that end, let’s tabulate the the 2x2 matrices (contingency matrices) for each comorbidity (yes/no) vs. responder (yes/no). For convenience, proportions (%) are depicted.
## [1] "Depression"
##
## 1 0
## 0 0.38 0.55
## 1 0.04 0.04
## [1] "PanicDisorder"
##
## 1 0
## 0 0.36 0.55
## 1 0.05 0.04
## [1] "SocialPhob"
##
## 1 0
## 0 0.38 0.54
## 1 0.04 0.05
## [1] "SpecificPhob"
##
## 1 0
## 0 0.32 0.55
## 1 0.09 0.04
## [1] "TourettesTics"
##
## 1 0
## 0 0.39 0.54
## 1 0.02 0.05
## [1] "ADHD"
##
## 1 0
## 0 0.39 0.50
## 1 0.02 0.09
## [1] "GAD"
##
## 1 0
## 0 0.36 0.54
## 1 0.05 0.05
## [1] "responder_3m"
##
## 1 0
## 0 0.00 0.59
## 1 0.41 0.00
## [1] "responder_3m_f"
##
## 1 0
## 1 0.41 0.00
## 0 0.00 0.59
Wait a minute, it looks as if there a few persons where responder_3m == 1! Does that mean, most participants did not respond (ie., no success)? ___
Hm, let’s divide that up for each comorbidity, and plot it:
Hoaza! That looks strange! Can that be? Surely there must be some bug, either in my code, what may well be the case (Deus adiuvet me), or in the data. ___
Let’s look at it from some other perspective, different code, and plot it again, and see what happens:
And what it about if we eyeball the plain number? The table shows the frequencies for treatment success/failure as a contigency of comorbidity.
| key | responder_3m | n |
|---|---|---|
| ADHD | 0 | 33 |
| ADHD | 1 | 23 |
| ADHD | NA | 5 |
| Agoraphobia | 0 | 33 |
| Agoraphobia | 1 | 23 |
| Agoraphobia | NA | 5 |
| Depression | 0 | 33 |
| Depression | 1 | 23 |
| Depression | NA | 5 |
| Dystymia | 0 | 33 |
| Dystymia | 1 | 23 |
| Dystymia | NA | 5 |
| EatingDis | 0 | 33 |
| EatingDis | 1 | 23 |
| EatingDis | NA | 5 |
| GAD | 0 | 33 |
| GAD | 1 | 23 |
| GAD | NA | 5 |
| ODD | 0 | 33 |
| ODD | 1 | 23 |
| ODD | NA | 5 |
| PanicDisorder | 0 | 33 |
| PanicDisorder | 1 | 23 |
| PanicDisorder | NA | 5 |
| PTSD | 0 | 33 |
| PTSD | 1 | 23 |
| PTSD | NA | 5 |
| SeparationAnx | 0 | 33 |
| SeparationAnx | 1 | 23 |
| SeparationAnx | NA | 5 |
| SocialPhob | 0 | 33 |
| SocialPhob | 1 | 23 |
| SocialPhob | NA | 5 |
| SpecificPhob | 0 | 33 |
| SpecificPhob | 1 | 23 |
| SpecificPhob | NA | 5 |
| TourettesTics | 0 | 33 |
| TourettesTics | 1 | 23 |
| TourettesTics | NA | 5 |
Hm, the same picture emerges: With comorbidity always 23 cases, without comorbidity also 33 cases. Somewhere there must be a bug…
4 Most important variables (narrow data set)
4.1 Type of most important variables
Let’s focus on the most important variables, to make life easier.
That should be all sum scores. Let’s look for them:
Ok, the variables are CYBOCS_pre_sum, ChOCI_R_C_sumsym_PRE, ChOCI_R_C_sumimp_PRE, EWSASC_sum_PRE, SCAS_S_C_sum_PRE, CDI_S_sum_PRE, ChOCI_R_P_sumsym_PRE, ChOCI_R_P_sumimp_PRE, FAS_PR_sum_PRE, EWSASP_sum_PRE, SCAS_S_P_sum_PRE. In total, 11 variables.
We can probably safely ignore ID. We should include basic and demographic variables:
Which gives us group, sex, age, Birthcountry, Education_parent, OCDonset, yearswithOCD, contact, distance, medication, medication_yesno, treatm_exp, OCD_treatm_exp, responder_3m, CYBOCS_3m, another 15 variables.
Of particular interest are of course responder_3m, CYBOCS_3m (outcomes) and group (experimental factor).
Next, let’s name the comorbidities.
These are Depression, Dystymia, PanicDisorder, Agoraphobia, SeparationAnx, SocialPhob, SpecificPhob, PTSD, TourettesTics, ADHD, ODD, EatingDis, GAD.
In total, 3 sets of variables then: basic variables (including outcome and experimental variables), sum scores of psychometric battery, and comorbidity.
In total, 39 Variables: group, sex, age, Birthcountry, Education_parent, OCDonset, yearswithOCD, contact, distance, medication, medication_yesno, treatm_exp, OCD_treatm_exp, responder_3m, CYBOCS_3m, CYBOCS_pre_sum, ChOCI_R_C_sumsym_PRE, ChOCI_R_C_sumimp_PRE, EWSASC_sum_PRE, SCAS_S_C_sum_PRE, CDI_S_sum_PRE, ChOCI_R_P_sumsym_PRE, ChOCI_R_P_sumimp_PRE, FAS_PR_sum_PRE, EWSASP_sum_PRE, SCAS_S_P_sum_PRE, Depression, Dystymia, PanicDisorder, Agoraphobia, SeparationAnx, SocialPhob, SpecificPhob, PTSD, TourettesTics, ADHD, ODD, EatingDis, GAD.
4.2 Coarse model
Vague defined, the model can be described as consisting of these predictors: demographics, psychometric scales, treatment (group), comorbities. The outcome is treatment response.
coarse model
4.3 Missing values and sum scores
When tallying up sum scores, missing values cause problems. Assume 10 items to summed up. What if I have not responded to 9 items? If you count “zero” for the missing values, you will dramatically underestimate my true score. I wonder how the sum scores have been built here.
4.3.1 ChOCI scale (self-rated comorbidity)
The most items appear in the ChOCI scale. So let’s look there first.
Ok, good, no missings. Have they been replaced somehow? Where the participants forced to give some answer? This might be of interest for gauging the psychometric quality of the scale.
4.3.2 CYBOCS OCD symptoms
| item | n_na |
|---|---|
| CYBOCS_pre_OBS | 0 |
| CYBOCS_pre_COMP | 0 |
| CYBOCS_pre_sum | 0 |
| CYBOCS_pre_insight | 2 |
| CYBOCS_pre_avoid | 6 |
| CYBOCS_3m | 5 |
Hm, here we find some missing values. So what was done to prevent bias here? We should follow up on that.
4.3.3 EWSASC (functioning)
Same procedure…
| item | n_na |
|---|---|
| EWSASC_schoolandwork_PRE | 0 |
| EWSASC_everydaysituations_PRE | 0 |
| EWSASC_social_PRE | 0 |
| EWSASC_leisuretime_PRE | 0 |
| EWSASC_family_PRE | 0 |
| EWSASC_sum_PRE | 0 |
Ok, no NA’s.
4.3.4 SCAS (Anxiety)
| item | n_na |
|---|---|
| SCAS_S_C_1_PRE | 0 |
| SCAS_S_C_2_PRE | 0 |
| SCAS_S_C_3_PRE | 0 |
| SCAS_S_C_4_PRE | 0 |
| SCAS_S_C_5_PRE | 0 |
| SCAS_S_C_6_PRE | 0 |
| SCAS_S_C_7_PRE | 0 |
| SCAS_S_C_8_PRE | 0 |
| SCAS_S_C_9_PRE | 0 |
| SCAS_S_C_10_PRE | 0 |
| SCAS_S_C_11_PRE | 0 |
| SCAS_S_C_12_PRE | 0 |
| SCAS_S_C_sum_PRE | 0 |
| SCAS_S_P_1_PRE | 0 |
| SCAS_S_P_2_PRE | 0 |
| SCAS_S_P_3_PRE | 0 |
| SCAS_S_P_4_PRE | 0 |
| SCAS_S_P_5_PRE | 0 |
| SCAS_S_P_6_PRE | 0 |
| SCAS_S_P_7_PRE | 0 |
| SCAS_S_P_8_PRE | 0 |
| SCAS_S_P_9_PRE | 0 |
| SCAS_S_P_10_PRE | 0 |
| SCAS_S_P_11_PRE | 0 |
| SCAS_S_P_12_PRE | 0 |
| SCAS_S_P_sum_PRE | 0 |
No NA’s.
4.3.5 CDI (Depression)
| item | n_na |
|---|---|
| PanicDisorder | 0 |
| CDI_S_1_PRE | 0 |
| CDI_S_2_PRE | 0 |
| CDI_S_3_PRE | 0 |
| CDI_S_4_PRE | 0 |
| CDI_S_5_PRE | 0 |
| CDI_S_6_PRE | 0 |
| CDI_S_7_PRE | 0 |
| CDI_S_8_PRE | 0 |
| CDI_S_9_PRE | 0 |
| CDI_S_10_PRE | 0 |
| CDI_S_sum_PRE | 0 |
No NA’s.
4.3.6 FAS (family accomodation)
| item | n_na |
|---|---|
| FAS_PR_1_PRE | 0 |
| FAS_PR_2_PRE | 0 |
| FAS_PR_3_PRE | 0 |
| FAS_PR_4_PRE | 0 |
| FAS_PR_5_PRE | 0 |
| FAS_PR_6_PRE | 0 |
| FAS_PR_7_PRE | 0 |
| FAS_PR_8_PRE | 0 |
| FAS_PR_9_PRE | 0 |
| FAS_PR_10_PRE | 0 |
| FAS_PR_11_PRE | 0 |
| FAS_PR_12_PRE | 0 |
| FAS_PR_sum_PRE | 0 |
No NA’s.
4.3.7 EWSASP (functioning, 2nd scale)
| item | n_na |
|---|---|
| EWSASP_schoolandwork_PRE | 0 |
| EWSASP_everydaysituations_PRE | 0 |
| EWSASP_social_PRE | 0 |
| EWSASP_leisuretime_PRE | 0 |
| EWSASP_family_PRE | 0 |
| EWSASP_sum_PRE | 0 |
No NA’s.
4.3.8 SCAS (Anxiety)
| item | n_na |
|---|---|
| SCAS_S_C_1_PRE | 0 |
| SCAS_S_C_2_PRE | 0 |
| SCAS_S_C_3_PRE | 0 |
| SCAS_S_C_4_PRE | 0 |
| SCAS_S_C_5_PRE | 0 |
| SCAS_S_C_6_PRE | 0 |
| SCAS_S_C_7_PRE | 0 |
| SCAS_S_C_8_PRE | 0 |
| SCAS_S_C_9_PRE | 0 |
| SCAS_S_C_10_PRE | 0 |
| SCAS_S_C_11_PRE | 0 |
| SCAS_S_C_12_PRE | 0 |
| SCAS_S_C_sum_PRE | 0 |
| SCAS_S_P_1_PRE | 0 |
| SCAS_S_P_2_PRE | 0 |
| SCAS_S_P_3_PRE | 0 |
| SCAS_S_P_4_PRE | 0 |
| SCAS_S_P_5_PRE | 0 |
| SCAS_S_P_6_PRE | 0 |
| SCAS_S_P_7_PRE | 0 |
| SCAS_S_P_8_PRE | 0 |
| SCAS_S_P_9_PRE | 0 |
| SCAS_S_P_10_PRE | 0 |
| SCAS_S_P_11_PRE | 0 |
| SCAS_S_P_12_PRE | 0 |
| SCAS_S_P_sum_PRE | 0 |
No NA’s.
5 Interocular Trauma Test
5.1 Outcome: responder_3m
Before applying some sophisticated (aka esoteric) models, let’s perform the intraocular trauma test for the data: let’s see whether the effect is so crisp that it hits us right between the eyes. That is., is there an association between group and response?
Because for the fun of it (and because the question if of particular interest), let’s plot from different point of views.
Hm, it appears as if the experimental group was less successful than the control group. That result might hit us between the eyes… But one would certainly hope for something the other way round.
The bare numbers:
| group | responder_3m | n |
|---|---|---|
| ICBT | 0 | 21 |
| ICBT | 1 | 10 |
| ICBT | NA | 2 |
| waitlist | 0 | 12 |
| waitlist | 1 | 13 |
| waitlist | NA | 3 |
5.2 Outcome: CYBOCS_3m
For this outcome, it seems as if there was some (slight?) advantage for the treatment group. However, the overlap is substantial.
Here come the bare figures:
| group | group_mean | group_md | group_sd | group_IQR |
|---|---|---|---|---|
| ICBT | 14.22581 | 14 | 5.903161 | 7 |
| waitlist | 12.56000 | 12 | 6.807349 | 9 |